The blow-up of electromagnetic fields in 3-dimensional invisibility cloaking for Maxwell's equations (Q2790416)

Let a domain \(\Omega\subset\mathbb R^3\) contains a domain \(D\Subset\Omega\), \(D_1=\Omega\backslash\overline{D}\). The authors consider Maxwell's equations \(\operatorname{curl}E-i\omega B=0\), \(\operatorname{curl}H+i\omega D=J\) in \(D\cup D_1\) where also the constitutive relations \(D=\varepsilon E\) and \(B=\mu H\) are given. It is assumed that the eigenvalues of \(\varepsilon(\mathbf x)\) and \(\mu(\mathbf x)\) degenerate to zero at \(\partial D\). The boundary conditions on \(\partial D\) and spaces of solutions are discussed. Effects of the blow up of solutions and applications to cloaking are considered.